Satellite Motion: Speed & Period Video Lessons

Concept

Problem: Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times.As a satellite spirals inward, does it speed up, slow down, or maintain the same speed?

FREE Expert Solution

In this problem, we need to know Kepler's law of planetary motion, which is stated as:

$\overline{)\begin{array}{rcl}{\mathbf{T}}^{\mathbf{2}}& {\mathbf{\propto }}& {\mathbf{R}}^{\mathbf{3}}\\ {\mathbf{T}}& {\mathbf{\propto }}& {\mathbf{R}}^{\frac{\mathbf{2}}{\mathbf{3}}}\end{array}}$, where T is the time period and R is the radius of the orbit.

Problem Details

Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times.

As a satellite spirals inward, does it speed up, slow down, or maintain the same speed?